A362579 Numbers k such that the decimal expansion of 1/k does not contain the digit 5.

1, 3, 5, 6, 9, 10, 11, 12, 13, 15, 21, 24, 25, 27, 30, 33, 36, 37, 41, 44, 45, 48, 50, 52, 55, 60, 72, 73, 75, 77, 84, 88, 90, 91, 96, 99, 100, 101, 110, 111, 120, 123, 125, 130, 135, 137, 143, 144, 150, 159, 165, 205, 208, 210, 216, 225, 231, 237, 239, 240, 250, 259, 264, 270, 271, 273, 275, 288

Offset

1,2

Comments

If k is a term, then so is 10*k.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2692 (n = 1..1000 from Robert Israel)

Example

a(8) = 12 is a term because 1/12 = 0.08333... does not contain the digit 5.

Maple

filter:= proc(n) local q;
  q:= NumberTheory:-RepeatingDecimal(1/n);
  not(member(5, RepeatingPart(q)) or member(5, NonRepeatingPart(q)))
end proc:
select(filter, [$1..300]);

Mathematica

Select[Range[500], FreeQ[First[RealDigits[1/#]], 5] &] (* Paolo Xausa, Apr 23 2024 *)

Prog

(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A362579_gen(startvalue=1): # generator of terms >= startvalue
    for a in count(max(startvalue, 1)):
        m2, m5 = (~a&a-1).bit_length(), multiplicity(5, a)
        k, m = 10**max(m2, m5), 10**n_order(10, a//(1<<m2)//5**m5)-1
        if not('5' in str(c:=k//a) or '5' in str(m*k//a-c*m)):
            yield a
A362579_list = list(islice(A362579_gen(), 20)) # Chai Wah Wu, May 01 2023

Crossrefs

Complement of A353441.

Sequence in context: A321885 A161182 A267312 * A331386 A331916 A371127

Adjacent sequences: A362576 A362577 A362578 * A362580 A362581 A362582

Keyword

nonn,base

Author

Robert Israel, Apr 25 2023

Status

approved